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About influence of the choice of numerical flow in the DG method for the solution of problems with shock waves

  • Mikhail M., Krasnov (Keldysh Institute of Applied Mathematics of RAS) ;
  • Marina E., Ladonkina (Keldysh Institute of Applied Mathematics of RAS) ;
  • Olga A., Nekliudova (Keldysh Institute of Applied Mathematics of RAS) ;
  • Vladimir F., Tishkin (Keldysh Institute of Applied Mathematics of RAS)
  • Received : 2022.02.20
  • Accepted : 2022.09.01
  • Published : 2022.09.25
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Abstract

This study compares various ways of calculating flows for the problems with the presence of shock waves by first-order schemes and higher-order DG method on the tests from the Quirk list, namely: Quirk's problem and its modifications, shock wave diffraction at a 90 degree corner, the problem of double Mach reflection. It is shown that the use of HLLC and Godunov's numerical schemes flows in calculations can lead to instability, the Rusanov-Lax-Friedrichs scheme flow can lead to high dissipation of the solution. The most universal in heavy production calculations are hybrid schemes flows, which allow the suppression of the development of instability and conserve the accuracy of the method.

Keywords

Acknowledgement

The research described in this paper was financially supported by the Russian Science Foundation (grant No. 21-11-00198) The calculations were performed on a hybrid supercomputer K-60 at the KIAM RAS (Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences) Collective Usage Centre.

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